let j be Element of NAT ; :: thesis: for N being non empty with_non-empty_elements set
for S being non empty IC-Ins-separated halting AMI-Struct of N
for p being NAT -defined the Instructions of b₂ -valued Function
for s being State of S st LifeSpan (p,s) <= j & p halts_on s holds
Comput (p,s,j) = Comput (p,s,(LifeSpan (p,s)))
let N be non empty with_non-empty_elements set ; :: thesis: for S being non empty IC-Ins-separated halting AMI-Struct of N
for p being NAT -defined the Instructions of b₁ -valued Function
for s being State of S st LifeSpan (p,s) <= j & p halts_on s holds
Comput (p,s,j) = Comput (p,s,(LifeSpan (p,s)))
let S be non empty IC-Ins-separated halting AMI-Struct of N; :: thesis: for p being NAT -defined the Instructions of S -valued Function
for s being State of S st LifeSpan (p,s) <= j & p halts_on s holds
Comput (p,s,j) = Comput (p,s,(LifeSpan (p,s)))
let p be NAT -defined the Instructions of S -valued Function; :: thesis: for s being State of S st LifeSpan (p,s) <= j & p halts_on s holds
Comput (p,s,j) = Comput (p,s,(LifeSpan (p,s)))
let s be State of S; :: thesis: ( LifeSpan (p,s) <= j & p halts_on s implies Comput (p,s,j) = Comput (p,s,(LifeSpan (p,s))) )
assume that
A1: LifeSpan (p,s) <= j and
A2: p halts_on s ; :: thesis: Comput (p,s,j) = Comput (p,s,(LifeSpan (p,s)))
CurInstr (p,(Comput (p,s,(LifeSpan (p,s))))) = halt S by A2, Def14;
hence Comput (p,s,j) = Comput (p,s,(LifeSpan (p,s))) by A1, Th6; :: thesis: verum